Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 2 - Section 2.5 - An Introduction to Problem Solving - Exercise Set - Page 167: 43


The price of the car before taxes is $22,500.

Work Step by Step

First, we need to define our unknown. What we want to find out the price of the car before taxes, which we shall designate as $x$: This is our unknown. We will need to add the amount of the tax to the price of the car before taxes to get the final price of $23,850$ dollars. The tax is $6$%, so the amount of taxes added to the price of the car can be given by the expression (6%)$(x)$. We cannot work with percentages, so we change the percent into a decimal. We do this by dividing the percentage by $100$ to get rid of the percentage sign. We now have the percentage changed to the decimal $0.06$. We can now set up the following equation to find the price of the car before the sales tax was added: $$x + 0.06x = 23,850$$ We combine like terms: $$1.06x = 23,850$$ To solve for $x$, we divide both sides of the equation by $1.06$: $$x = 22,500$$ The price of the car before taxes is $22,500.
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